A water-abrasive suspension cutting facility which comprises a lock with a lock chamber permitting the introduction of abrasive agent in the high-pressure region of the cutting facility during running operation is known from WO 2013/037405. With such a facility, the difficultly arises of filling the lock chamber with abrasive agent and emptying it again, in a sufficiently rapid manner, in order to be able to bring an adequately large quantity of abrasive agent into the high pressure region of the facility per unit of time.